We study the temporal variability of water transfer through the infiltration zone of a karst aquifer by estimating the impulse response of the system using cross-correlogram analyses between rainfall and piezometric level time series. We apply a sliding-window cross-correlation method, which calculates cross-correlograms on partially superposed short time series windows. We apply this method for rainfall and piezometric level time series at six boreholes in a fractured karstic aquifer located in Burgundy, France. Based on cross-correlogram functions, we obtain a time series of response time. At most of the boreholes, the cross-correlation functions change over time, and the response times vary seasonally, being shorter during the summer. This unusual structure can be partly explained by the seasonal variability in rainfall intensity, which is higher during the summer (May–September), inducing the seasonal behaviour of the epikarst. During the summer, when rainfall intensity is higher, the epikarst is more easily and quickly saturated. This induces an increase in lateral water transfer within the epikarst and an increase in concentrated fast flows. We also show that the response time seems to tend towards a limit which represents the maximum saturation of the epikarst.